Cut out surplus material
Boolean operations would work well in this case.

Alternatively you could also use the Knife Project operator on your mesh. It basically uses the outline of another object (mesh or curve) and cuts the editing mesh through its silhouette.

It's workflows goes like:


Select 'knife object' (cutting shape)
Select object to be cut (without deselecting the previous one)
Enter Edit Mode on the object to be cut
Adjust the view accordingly, the cutting process is view based (dependent on the current viewport view angle and perspective mode), if desired switch to User View with Numpad 5 for an undistorted true size cut.
Open the Space Bar menu and call the operator Knife Project
Tick the option Cut Through so all faces are cut, even the background ones
Select the remaining geometry and manually delete it.